On commuting families of nonexpansive operators
Proc. Amer. Math. Soc. 84 (1982), 373-376
Primary 47H09; Secondary 47H10
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Abstract: For each , , there exist a weakly compact, convex subset of and a family of nonexpansive operators of into such that there is no common fixed point for the whole family but any (finite) strict subfamily admits a common fixed point.
- D. E. Alspach, A fixed point free nonexpansive map, Proc. Amer. Math. Soc. 82 (1981), 423-424. MR 612733 (82j:47070)
- N. Dunford and J. T. Schwartz, Linear operators. I, Interscience, New York, 1958.
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Common fixed point,
weakly compact sets,
© Copyright 1982
American Mathematical Society